Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare a safe, idempotent, read-only open-world operation, so the bar is lower, and the description still adds real context: a per-call price of $0.001 USDC via x402 on Solana, an equivalent HTTPS endpoint, and the edge-case rule that a zero modulus is rejected. The only gap is that it doesn't explain what a reduced (mod) result looks like beyond 'reduces the count'.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Five short sentences, front-loaded with the definition and examples before constraints, pricing, and the alternate endpoint. The odd-parts identity is interesting but not strictly needed to invoke the tool; otherwise there is no filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description does need to imply the return value, and it does so by defining the result as a count, plus examples. Combined with the range, modulus rule, pricing, and endpoint information, an agent has enough to call correctly; only the exact shape of a mod-reduced result is left implicit.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must carry the burden, and it largely does: it gives n's valid range (0–2000) and explains the mod parameter's effect and its zero-rejection rule. It doesn't clarify that mod is a digit-string bounded to 200 characters for arbitrary-precision arithmetic, which the schema implies but never explains.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description states precisely what is computed: the count of partitions of n into distinct positive parts, with examples q(0)=1 and q(5)=3 that pin the semantics. It is clear on its own terms but never names the closely related siblings (partition, partition_parts, overpartition), so an agent must infer the distinction from the mathematical definition rather than from an explicit contrast.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is only implied: the valid domain (n from 0 to 2000) and the optional modulus are stated, but nothing tells the agent when to choose this over partition or overpartition, or when the mod variant is appropriate. There are no exclusions or alternative routing hints beyond the practical range constraint.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.